That is true in vacuum, but not in media. In a medium, different wavelengths travel at different speeds (this is called dispersion), so different wavelengths get different refractive indices. This is why a prism splits white light into different colors, for example.

Refractive index depends on the speed of light travelling through that medium.It also depends on the wave length of light.If refractive index of water is 1.33,then for which wavelength is this?

We all know that refractive index can be calculated with n=c/v and that the speed of light is
c=λf. To understand this question we need to see that light technically does not "slow down" when it passes through refractive areas. Instead it takes longer due to the thickness of the particles the light needs to bounce through. The variable v in n=c/v is just the measurement of the distance over the time that the light takes to pass through the area.

We all know that refractive index can be calculated with n=c/v and that the speed of light is
c=λf. To understand this question we need to see that light technically does not "slow down" when it passes through refractive areas. Instead it takes longer due to the thickness of the particles the light needs to bounce through. The variable v in n=c/v is just the measurement of the distance over the time that the light takes to pass through the area.

We all know that refractive index can be calculated with n=c/v and that the speed of light is
c=λf. To understand this question we need to see that light technically does not "slow down" when it passes through refractive areas. Instead it takes longer due to the thickness of the particles the light needs to bounce through. The variable v in n=c/v is just the measurement of the distance over the time that the light takes to pass through the area.

I'm curious, is there any natural or intuitive way to think of dispersion in this picture? Why should blue light need a different number of bounces than red light, for example?

Light technically does slow down. What is the advantage of saying it doesn't?

The advantage is that you don't have to explain how the light accelerates to c after leaving the medium.

Basically, ray diagrams and everyday experiences tell us that light travels in a straight line so you would need some kind of force at the interface. Or you could say that the light doesn't take a perfectly straight path on the microscopic level due to these bounces, so the average (net) speed decreases in the medium.

The advantage is that you don't have to explain how the light accelerates to c after leaving the medium.

Basically, ray diagrams and everyday experiences tell us that light travels in a straight line so you would need some kind of force at the interface. Or you could say that the light doesn't take a perfectly straight path on the microscopic level due to these bounces, so the average (net) speed decreases in the medium.

Actually it's much easier in calculations if we say speed of light changes(even if it doesn't),like the refractive index equation.If we are to account everything in a calculation,it would be impossible

Actually it's much easier in calculations if we say speed of light changes(even if it doesn't),like the refractive index equation.If we are to account everything in a calculation,it would be impossible

Certainly! I'm not advocating that you should account for everything in calculations, but I am advocating to keep in mind that our simple models of physics aren't the whole truth.

One way of thinking of things may be advantageous for calculations, another less so. The first way doesn't even have to make sense, it could just be a heuristic for how to calculate things. But if the second picture is advantageous in that it makes different concepts and facts of physics consistent and hence possible to understand, it also has its value. In fact, it may be advantageous to think about the physics using that picture, and still doing the calculations in the simplified model.

We all know that refractive index can be calculated with n=c/v and that the speed of light is
c=λf. To understand this question we need to see that light technically does not "slow down" when it passes through refractive areas. Instead it takes longer due to the thickness of the particles the light needs to bounce through. The variable v in n=c/v is just the measurement of the distance over the time that the light takes to pass through the area.

That's hogwash. There is no "bouncing around". Light really slows down in a medium.

I think people need to understand what we mean when we talk about the "speed of light" in this context. There is a need here to really understand what is meant by the group velocity of light, such as when you send a light pulse out, either in vacuum or through a medium. What do you think is measured here when we try to detect the "speed" of this light?

In the equation above, ##n = c/v_{ph}##, ##v_{ph}## is the phase speed.
Going along ZapperZ's point, to actually measure a speed, you have to send some kind of light pulse through the medium. Any light pulse will contain a broad spectrum of frequencies, and the pulse will come out very distorted on the other end of the medium. If there is a dominant frequency in the light pulse, then the phase velocity of the dominant frequency will be useful for calculating when most of the energy of the initial pulse gets to the detector.

I suppose the very front of the light pulse (defined as where the electromagnetic field is nonzero) will pass through the medium at a speed c, but this front will be severely attenuated. On the other end, the back of the pulse will be slowed way down, so the pulse is dispersed.

Refractive index depends on the speed of light travelling through that medium.It also depends on the wave length of light.If refractive index of water is 1.33,then for which wavelength is this?

I should say that the speed of light depends upon the refractive index, rather than the way round you are putting it. The refractive index is a property of the medium. (Which will always very to some extent with wavelength - which is one reason that good camera lenses, with low chromatic aberration, cost an arm and a leg) The RI will be quoted for a particular wavelength, if it has been measured accurately enough to make a difference.
See the graph near the end of this link.

It is my understanding that blue light has a greater index of refraction than the other wavelengths because its frequency is closer to the natural resonant frequency of electrons in a material, violet to uv.
When light enters a medium the electric field causes the electrons in the material to oscillate proportional to the materials permittivity.
This oscillation of charges produces a wave of the same frequency but slightly out of phase with the original wave.
(The sum of these waves is a wave with the same frequency and a shorter wavelength causing a slowing of the wave).*
Permittivity is related to the dielectric constant.
n = c/v = √εμ
μ ≈ 1 for most materials in the light range

* If this is not correct, please correct. If it is correct can someone show how the sum of two waves of same
frequency slightly out of phase produces a wave with shorter wavelength. I thought only the
amplitude is affected.

I also don't quite understand this discussion on the distinction between "true" speed of light and it's apparent value in a medium.
E.g. when you observe a supernova, are detected hours after the neutrinos due to their interaction with the interstelar medium. I think it would be strange not to say that they have a lower speed.

I suppose the very front of the light pulse (defined as where the electromagnetic field is nonzero) will pass through the medium at a speed c, but this front will be severely attenuated. On the other end, the back of the pulse will be slowed way down, so the pulse is dispersed.

There is a very interesting calculation in Arnold Sommerfelds classic lectures on Optics.

I also don't quite understand this discussion on the distinction between "true" speed of light and it's apparent value in a medium.
E.g. when you observe a supernova, are detected hours after the neutrinos due to their interaction with the interstelar medium. I think it would be strange not to say that they have a lower speed.

I thought that the OP was just about the wavelength at which the refractive index is quoted. That velocity ratio is defined in terms of phase velocity and an endless wave train, afaik, which is what the simple Snell's Law diagram is based on. There seems to have been a bit of 'inflation' in the thread which risks confusing the guy with the simple question.